It is interesting. DNA itself could be analogous to the tape that a Turing machine reads one cell at a time. The alphabet in each cell is finite (ATCG).
Not a biologist but the whole thing reminded me of a NOP sled
If you used your nop sled in a stenographic fashion (ie: each type of NOP can be decoded as some piece of information) you would be pretty close when it comes to RNA virus replication. For that matter, some computer viruses purposely mutate the nop sled to avoid creating scan strings, so there are a number of similarities to be had as long as each mutation still performs the necessary function.